Question

Suppose your friends have the following ice cream flavor preferences: 70% of your friends like chocolate (C). The remaining do not like chocolate. 40% of your friends like sprinkles (S) topping. The remaining do not like sprinkles. 25% of your friends who like Chocolate (C) also like sprinkles (S). Of the friends who like sprinkles, what proportion of this group likes chocolate

Answer 1

Answer:

The proportion of this group that likes chocolate is 0.625.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Likes sprinkles

Event B: Likes chocolate

25% of your friends who like Chocolate (C) also like sprinkles (S).

This means that $P(A \cap B) = 0.25$

40% of your friends like sprinkles (S) topping.

This means that $P(A) = 0.4$

Of the friends who like sprinkles, what proportion of this group likes chocolate

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.25}{0.4} = 0.625$

The proportion of this group that likes chocolate is 0.625.